Tracking collective cell motion by topological data analysis

Abstract

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments, spreading tests exhibit finger formation in the moving interfaces, swirls in the velocity field, and the polar order parameter and correlation and swirl lengths increase with time. Cells inside the tissue have smaller area than those at the interface, as observed in recent experiments. In antagonistic migration assays, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to numerical simulations. We use time series of numerical simulation data to automatically group, track and classify advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These topological data analysis techniques are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

arXiv comment34 pages, 25 figures, the final version will appear in PLoS Computational Biology

References in corpus (13)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• Motility-driven glass and jamming transitions in biological tissues
• Physical Models of Collective Cell Migration
• Arrested phase separation in reproducing bacteria: a generic route to pattern formation?
• Topological Data Analysis of Biological Aggregation Models
• Emergent structures and dynamics of cell colonies by contact inhibition of locomotion
• Deep Learning with Topological Signatures
• Topological data analysis of zebrafish patterns
• Active Fingering Instability in Tissue Spreading
• Giant fluctuations and structural effects in a flocking epithelium
• Contrarian compulsions produce time dependent flocking of active particles
• Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances

Cited by in corpus (7)

• Noise robustness of persistent homology on greyscale images, across filtrations and signatures
• Anomalous angiogenesis in retina
• Coarse-graining the vertex model and its response to shear
• Persistent homology and the shape of evolutionary games
• Soliton approximation in continuum models of leader-follower behavior
• Hierarchical topological clustering
• Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics